Here's a suggestion: make an appliance with two NTC thermistors, fairly close but not too close to each other -- say 10 cm/4 inches away so that they're exposed to the same temperature, but don't influence each other.
The first one should be biased with a low current, either from a constant-current source or a resistive divider. Either way, you should use the lowest current that is practical to measure with around 0.5 degree Celsius/1 degree Fahrenheit accuracy -- I'm certainly talking sub-mA here, probably in the range of 10s of uA. This avoids any kind of self-heating effect.
The second one should be biased with a constant current source that is a bit higher -- you should size it according to your NTC's R25 parameter, thermal resistance, etc. I estimate 5 to 10 mA should work for an NTC with R25 = 10kΩ. This will significantly self-heat the second NTC, but after a quick transient period it should settle to a temperature that's X degrees above ambient, where the exact value of X depends on all factors mentioned; you're shooting for a fairly high value, but not too high to risk exceeding the NTC's rated temperature. If X is not high enough, it's going to be hard distinguishing between a gentle breeze and random fluctuations.
Start by measuring X in an environment with still air. The effect of a breeze on the second NTC is to lower its thermal resistance, or in other words, reduce X. Whether the breeze is colder, hotter or the same temperature as ambient doesn't matter, because the first NTC is measuring the change in temperature due to the breeze. The point is to compare the difference between the temperature reported by the second and the first NTC. In still air it should always hover around X, but in case of a breeze, it should be detectably lower than X. The stronger the breeze, the more X will decrease.